Smooth transition type integral operators
type: Item
instance of: scholarly article
title: Smooth transition type integral operators
zbMATH Open document ID: 0709.45008
DOI: 10.1007/BF01078779
author: A. B. Nersesyan
author: Armen G. Kamalyan
publication date: 1989-01-01T00:00:00Z
review text: The paper investigates the integral operators of convolution type \((Ky)(x)=y(x)+\lambda (x)\int^{\infty}_{-\infty}k(x-t)y(t)dt\quad (y\in L_ 2(R)).\) Under the natural conditions on \(\lambda\) (x) and k(x) the connection of the operator k with integral operators on the semi-axis are found. In the particular case of \(\lambda (x)=t h(x/2+i\pi \beta /2)\) \((-1<\beta <1)\) from this follows the solution of the equation \(Ky=f\) which generalized the well-known Cherskij equation (corresponding to the case \(\lambda (x)=t h(x/2)).\) The matrix generalization of the operator of smooth transition is also solved. In the case of \(\lambda (x)=P(t h((x+i\pi \beta)/2))\) where P is a polynomial and \(\lambda (x)=\sum^{n}_{m=1}t h(x/2-\lambda_ m+i\pi \beta /2)\) \((\lambda_ m\in R)\) the investigation of the operator k reduces to the problem of factorization of certain matrices of functions.
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 4165689
zbMATH Keywords: smooth transition
zbMATH Keywords: matrix factorization
zbMATH Keywords: integral operators of convolution type
MaRDI profile type: Publication
cites work: Q3706407
cites work: Algebraic methods for Toeplitz-like matrices and operators
cites work: Q3866607
cites work: Q3215784
cites work: Estimates for translation invariant operators in \(L^p\) spaces
cites work: Q5827353
cites work: Q3782277
full work available at URL: https://doi.org/10.1007/bf01078779
OpenAlex ID: W2062155779
published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 4165689